Perturbation versus Differentiation Indices

Abstract

We discuss the relation between perturbation and differentiation indices for overdetermined systems of differential equations based on the formal theory. We show how the Cartan normal form of an involutive system can be used to extend the notion of an underlying equation from differential algebraic equations to partial differential equations. This allows us to generalise results of Campbell and Gear on the relation between perturbation and differentiation indices to systems of partial differential equations.